Models for Geostatistical Binary Data: Properties and Connections

This article explores models for geostatistical data for situations in which the region where the phenomenon of interest varies is partitioned into two disjoint subregions. This is called a binary map. The goals of the article are 3-fold. First, a review is provided of the classes of models that have been proposed so far in the literature for geostatistical binary data as well as a description of their main features. A problems with the use of moment-based models is pointed out. Second, a generalization is provided of the clipped Gaussian random field that eases regression function modeling, interpretation of the regression parameters, and establishing connections with other models. The second-order properties of this model are studied in some detail. Finally, connections between the aforementioned classes of models are established, showing that some of these are reformulations (reparameterizations) of the other classes of models.